Don Reinersten poses this question in his excellent book the Principles of product development FLOW. Don read it in William Feller's book An introduction to probability theory and its applications.
The first graph plots the cumulative total on a single walk.
- Y-axis is cumulative total, marked -40,-20,0,20,40
- X-axis is walk step, marked 0,100,200,...,900,1000
The second graph plots the probabilities for the cumulative total after N flips at
- N=10 (orange line)
- N=30 (blue line)
- N=100 (red line)
- N=1000 (green line)
- Y-axis is probability, marked 0.00, 0.05, 0.10, 0.15, 0.20, 0.25
- X-axis is cumulative total, marked -125,-100,-75,-50,-25,0,25,50,75,100,125
over time queues will randomly spin out of control ... You cannot rely on randomness to correct the problems that randomness creates.